Question

1 . 

a) 1/2 + 1/6 + 1/12 +....+1/x.(x+1) = 99/100

Answer 1

Bài 1: 

ĐKXĐ: \(x\notin\left\{0;-1\right\}\)

Ta có: \(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{x\left(x+1\right)}=\dfrac{99}{100}\)

\(\Leftrightarrow\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{x\left(x+1\right)}=\dfrac{99}{100}\)

\(\Leftrightarrow\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{99}{100}\)

\(\Leftrightarrow\dfrac{1}{1}-\dfrac{1}{x+1}=\dfrac{99}{100}\)

\(\Leftrightarrow\dfrac{x+1-1}{x+1}=\dfrac{99}{100}\)

\(\Leftrightarrow100x=99\left(x+1\right)\)

\(\Leftrightarrow100x-99x=99\)

hay x=99(thỏa ĐK)

Vậy: x=99